A common practice in the field of communication system analysis is to display a time-varying complex signal vector by plotting the real component and imaginary component parametrically as a function of time, as Cartesian coordinates on a plane. Such a display is frequently referred to as a polar display, independent of whether Cartesian or polar axes are used. For example, using a representative complex signal S(t)=I(t)+j*Q(t), the values I(t) and Q(t) are both plotted parametrically against time.
Frequently it is of interest to simultaneously display a reference waveform for comparison to a measured waveform. For example, the reference waveform might be a mathematically synthesized waveform that is optimum according to some criteria. FIG. 1 graphically depicts a reference waveform denoted as R(t) that is graphically overlaid with a corresponding measured waveform denoted as S(t), where the independent variable t spans some range, say, t1<t<t2. In this example, S(t) is shown as a solid line and R(t) is shown as a dashed line. While the diagram of FIG. 1 allows direct comparison of the measured waveform S(t) with the reference waveform R(t), this diagram is only useful if the time span, t2−t1, is relatively short. This is because as the time span of the measured and corresponding reference waveforms increases, the diagram or display becomes too complex to be of practical use. Specifically, the signal or line density increases beyond a level at which a viewer may readily discern useful information. In such a case, the resulting display is useful only for gross qualitative assessment, since line density is so great that individual vector paths are hidden within nearly coincident segments of the same waveform. Further, in this case, the use of reference waveforms is almost pointless, since the corresponding increase in line density further compounds the problem of visually conveying useful information.
One method of utilizing a reference waveform within the context of a long time duration is to subtract the reference waveform from the measured waveform such that the magnitude of the resulting difference is displayed as a function of time. While such a waveform is useful in finding a point at which a maximum difference occurs, any correlation between the difference or errors and the position of the measured waveform in a complex plane is lost.